Adaptive optimal controller design for an unbalanced UAV with slung load

Load transportation by Unmanned Aerial Vehicles is a research topic of great interest to the robotic community for its numerous applications in both the civilian and military fields. Attaching a cargo through an elastic cable to a small underactuated UAV such as a quadcopter, which is inherently an unstable system, increases its instability and its underactuated degrees of freedom by three. Moreover, the presence of imperfections in the system such as having the quadcopter’s center of gravity and the cable hanging point arbitrarily shifted from the quadcopter’s geometric centroid further complicates the system. In this paper, a new nonlinear nine degree-of-freedom mathematical model is formulated for a quadcopter when its center of gravity is shifted from its geometric centroid and when a cable-suspended load is attached at an arbitrary position. Thus, a novel adaptive controller based on Linear Quadratic Regulator is designed to control the position and attitude of the quadcopter while minimizing the swinging and radial motions of the suspended load. Subsequently, nonlinear simulations are conducted for three case studies: conventional quadcopter, quadcopter-payload system without imperfections, quadcopter-payload system with imperfections. Finally, the results are presented demonstrating the effectiveness of the proposed control strategy.